Volume 4 Number 4 (Jul. 2014)

Using Cross-Evaluations in Data Envelopment Analysis

Kim Fung Lam

Abstract—In data envelopment analysis (DEA), all efficient
decision making units (DMUs) have the same efficiency score
which are difficult to discriminate. Cross-efficiency can be used
to discriminate among efficient-DMUs. It also provides an
alternative efficiency ranking for inefficient-DMUs. However,
weight sets used for cross-efficiency may not be proper for
ranking DMUs. The reason for this is that alternate optimal
solutions for the weights exist for efficient-DMUs in DEA. The
weight sets for efficient-DMUs are usually picked arbitrarily by
linear programming (LP) software within the alternate optimal
region. It is highly unlikely that those weight sets obtained from
the LP software are the most suitable for performance measure.
Therefore, some researchers have proposed using secondary
objectives to search for more homogeneous or better weight sets
within the alternate optimal regions. This paper examines four
of those models and attempts to determine the accuracy of the
four models in estimating the performance rankings for DMUs
in DEA.